For high-dimensional data set with complicated dependency structures, the full likelihood approach often renders to intractable computational complexity. This imposes di±culty on model selection as most of the traditionally used information criteria require the evaluation of the full likelihood. We propose a composite likelihood version of the Bayesian information criterion (BIC) and establish its consistency property for the selection of the true underlying model. Under some mild regularity conditions, the proposed BIC is shown to be selection consistent, where the number of potential model parameters is allowed to increase to in¯nity at a certain rate of the sample size. Simulation studies demonstrate the empirical performance of this new BIC criterion, especially for the scenario that the number of parameters increases with the sample size.
Gao, X and Song, Peter Xuekun, "Composite likelihood Bayesian information criteria for model selection in high dimensional data" (April 2009). The University of Michigan Department of Biostatistics Working Paper Series. Working Paper 79.